THE METRIC SYSTEM
The metric system is a system for measuring volume, length, and mass. This system is based on
groups of ten, and its basic prefixes are as follows:
Unit Number Line
1000 100 10 1 0.1 0.01 0.001
Kilo- Hecto- Deca- Unit Deci- Centi- Milli-
(K) (h) (D) (d) (c) (m)
The units are:
volume - liter (l) for example: milliliter (ml)
length - meter (m) centimeter (cm)
mass - gram (g) kilogram (kg)
To convert from one prefix to another (milli- to centi-), find out how many of the smaller
prefix are in the larger (how many milligrams in a gram). To do this, look at the unit number line
above. There is a difference of a multiple of ten between each prefix. To find out how many
milligrams are in one gram, count over on the unit line, multiplying by ten for each step.
There are 1000 milligrams in 1 gram. You can use the same trick to go from a larger prefix
to a smaller prefix. (But remember, there are always more of the smaller prefix than the larger
prefix, so the number you get will be how many “smallers” are in the larger.) To go from
kilometers to centimeters, use the same process as above, going the opposite direction. (See
graphic representation on next page)
There are 100,000 centimeters in 1 kilometer. This can be used to convert from one prefix
to another. The problems can be set up so that the unwanted prefix will cancel out, leaving the
desired prefix.
Example 1: Change 50 cm to m.
1. Use the conversion 1 m = 100 cm by the method stated above.
2. Set up the problem with the prefix to be canceled on the bottom.
cm 100
m 1
cm 50 •
3. Cancel out the unwanted prefix.
100
m 1
50 •
4. Divide 50 by 100 ( = 0.5).
